Problem: Multiply the following complex numbers, marked as blue dots on the graph: $(5 e^{3\pi i / 4}) \cdot (2 e^{5\pi i / 12})$ (Your current answer will be plotted in orange.)
Multiplying complex numbers in polar forms can be done by multiplying the lengths and adding the angles. The first number ( $5 e^{3\pi i / 4}$ ) has angle $\frac{3}{4}\pi$ and radius $5$ The second number ( $2 e^{5\pi i / 12}$ ) has angle $\frac{5}{12}\pi$ and radius $2$ The radius of the result will be $5 \cdot 2$ , which is $10$ The angle of the result is $\frac{3}{4}\pi + \frac{5}{12}\pi = \frac{7}{6}\pi$ The radius of the result is $10$ and the angle of the result is $\frac{7}{6}\pi$.